Prandtl Meyer Expansion Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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Fluid calculations are especially sensitive to density, viscosity, geometry, pressure conventions, and unit systems. Prandtl Meyer Expansion Calculator narrows that problem to the relationship used on this page, making the displayed prandtl-meyer angle easier to audit against the inputs and the governing equation.

What this calculator does

The Prandtl Meyer Expansion Calculator uses Gamma (γ), Mach (M₁) to estimate the page’s Prandtl-Meyer angle from the fluid-mechanics relationship below. It is meant for a defined geometry and property set, so the useful part is not just the headline number but also whether your density, viscosity, dimensions, pressure reference, and flow convention match the model.

How to use it

Start with the fields that actually drive this result: Gamma (γ), Mach (M₁). Keep units consistent with the menus beside the fields and avoid mixing values measured under different conditions. After calculating, change one input at a time if you are comparing scenarios; that makes cause-and-effect much easier to see.

How the calculation works

The current page evaluates the Prandtl–Meyer function ν(M,γ) for a supersonic Mach number. The expression combines arctangent terms based on M²−1 and the specific-heat ratio.

Example

For M = 2 and γ = 1.4, the Prandtl–Meyer function is about 26.4°. Changing the visible turn-angle field alone does not make the present page solve a downstream Mach number; the headline is the ν(M,γ) value.

How to interpret the result

Interpret the Prandtl-Meyer angle within the fluid, geometry, pressure reference, and property values you entered. A numerically plausible answer can still be physically wrong if gauge/absolute pressure, diameter/radius, viscosity type, or unit convention is mismatched, so compare the result with the assumptions as well as the formula.

Limitations and notes

Theta and the upstream pressure/temperature/density fields do not currently drive a downstream expansion solution. The page evaluates the Prandtl–Meyer angle at the entered Mach number; it does not solve M2 or expanded thermodynamic state from a turn angle.